Most warmbloods have it naturally due to them being popular war horses in the medieval times.Dressage was invented then to make it seem like the army was moving when they weren't hope this answered your question
Well, it can Come naturally or be trained with dressage
Hey! I think not all of them have the natural fancy movements, it depends on the bloodlines and and breeding! They are selecting horses that have those movements to breed so more and more have that maturally!
And a good rider can bring a horse to those fancy movements too, Charlotte showed that in a masterclass (you can look it up on youtube)
The fast majority that I have dealt with seem to be born with it to some extent